20,757 research outputs found
Adaptive Probability Theory: Human Biases as an Adaptation
Humans make mistakes in our decision-making and probability judgments. While the heuristics used for decision-making have been explained as adaptations that are both efficient and fast, the reasons why people deal with probabilities using the reported biases have not been clear. We will see that some of these biases can be understood as heuristics developed to explain a complex world when little information is available. That is, they approximate Bayesian inferences for situations more complex than the ones in laboratory experiments and in this sense might have appeared as an adaptation to those situations. When ideas as uncertainty and limited sample sizes are included in the problem, the correct probabilities are changed to values close to the observed behavior. These ideas will be used to explain the observed weight functions, the violations of coalescing and stochastic dominance reported in the literature
Morse index and multiplicity of min-max minimal hypersurfaces
The Min-max Theory for the area functional, started by Almgren in the early
1960s and greatly improved by Pitts in 1981, was left incomplete because it
gave no Morse index estimate for the min-max minimal hypersurface.
We advance the theory further and prove the first general Morse index bounds
for minimal hypersurfaces produced by it. We also settle the multiplicity
problem for the classical case of one-parameter sweepouts.Comment: Cambridge Journal of Mathematics, 4 (4), 463-511, 201
A Generalized Sznajd Model
In the last decade the Sznajd Model has been successfully employed in
modeling some properties and scale features of both proportional and majority
elections. We propose a new version of the Sznajd model with a generalized
bounded confidence rule - a rule that limits the convincing capability of
agents and that is essential to allow coexistence of opinions in the stationary
state. With an appropriate choice of parameters it can be reduced to previous
models. We solved this new model both in a mean-field approach (for an
arbitrary number of opinions) and numerically in a Barabasi-Albert network (for
three and four opinions), studying the transient and the possible stationary
states. We built the phase portrait for the special cases of three and four
opinions, defining the attractors and their basins of attraction. Through this
analysis, we were able to understand and explain discrepancies between
mean-field and simulation results obtained in previous works for the usual
Sznajd Model with bounded confidence and three opinions. Both the dynamical
system approach and our generalized bounded confidence rule are quite general
and we think it can be useful to the understanding of other similar models.Comment: 19 pages with 8 figures. Submitted to Physical Review
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